Nonline-of-sight (NLOS) ultraviolet (UV) communication is expected to play a prominent role in wireless communications with enhanced connectivity due to the aerosol and strong molecular scattering and availability of large unlicensed bandwidth. We investigate the performance of NLOS UV co-operative communication over a log-normal fading channel by considering the channel estimation error, as experienced in practical UV communication systems. An analytical framework for a dual-hop amplify-and-forward UV NLOS cooperative relay is developed. We derive the closed-form expressions of lower-bound outage probability and the average symbol error rate for the energy efficient modulation schemes, such as hexagonal quadrature amplitude modulation (QAM) and rectangular QAM schemes. The derived analytical results are validated through the Monte Carlo simulations.